however, in the question it is not know that it is an induction and the value is also unknown! All you know is that there is a 10 ohm resistor and capacitance or inductance in series

You are given the waveforms from the oscilloscope for Ch1 (red) and Ch2 (green)

Ch1 (input Voltage) has the wave form 20sin(523.59t + 48°) [note: voltage does not start at 0 when t= 0]
Ch2 (the voltage drop across the resistor) is 5sin(523.59t)

Does this mean the voltage source is 48 degrees out of phase to the current? I don't understand this since this is the source of the current, it has to start at the same time right?

So if i wanted to work out "Is" it would simply be (5 < 0) / (10 < 0)
The voltage drop of the resistor divided by the resistance.
therefore being 0.5 A < 0 right? This agrees with the simulator when creating the circuit to suit these two waveforms.

however, how can i find out the impedance of the Inductor (if it really is an inductor)?

I have thought about it a bit more. Can this be a trick question? The question also asks to state the type of reactance Xc or Xl, I knew it is an inductor due to the voltage phase. But As Ch2 is zero phase, it give the above impedance (26.76522425+29.72579302j) so it could also that it is a 29.72579302 ohm impedance with a 16.76522425 ohm resistor right? They never stated this in the question though, so somehow i think there is something incorrect in my understanding of this circuit.

Edit////

Ah ha! i get it now, it is not an ideal inductor! Such a simple concept causes me hours of thinking and research. Goes to show theory isn't everything.
so how can i calculate the practical inductors impedance?? i know its going to be 16.76522425+29.72579302j impedance. And Its going to be around a 74mH Inductor but how do i calculate the real resistance side of the 74mH inductor at 83.333Hz ??